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Operator ideals related to absolutely summing and Cohen strongly summing operators. (English) Zbl 1373.47058
Summary: We study the ideals of linear operators between Banach spaces determined by the transformation of vector-valued sequences involving the new sequence space introduced by A. K. Karn and D. P. Sinha [Glasg. Math. J. 56, No. 2, 427–437 (2014; Zbl 1301.46004)] and the classical spaces of absolutely, weakly and Cohen strongly summable sequences. As applications, we prove a new factorization theorem for absolutely summing operators and a contribution to the existence of infinite-dimensional spaces formed by nonabsolutely summing operators is given.

##### MSC:
 47L20 Operator ideals 46B45 Banach sequence spaces 47B10 Linear operators belonging to operator ideals (nuclear, $$p$$-summing, in the Schatten-von Neumann classes, etc.)
##### Keywords:
Banach sequence spaces; operator ideals; summing operators
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